Modelling mathematics problem solving item responses using a multidimensional IRT model

Abstract

This research examined students' responses to mathematics problem-solving tasks and applied a general multidimensional IRT model at the response category level. In doing so, cognitive processes were identified and modelled through item response modelling to extract more information than would be provided using conventional practices in scoring items. More specifically, the study consisted of two parts. The first part involved the development of a mathematics problem-solving framework that was theoretically grounded, drawing upon research in mathematics education and cognitive psychology. The framework was then used as the basis for item development. The second part of the research involved the analysis of the item response data. It was demonstrated that multidimensional IRT models were powerful tools for extracting information from a limited number of item responses. A problem-solving profile for each student could be constructed from the results of IRT scaling.